The Duke’s title will eventually pass on to his youngest son the Earl of Wessex, but not until after the death of the Queen

In keeping with the Letters Patent issued – when George VI gave Philip the title in 1947 – the Prince of Wales, as the duke’s eldest son, inherits the title the Duke of Edinburgh, but on Charles’s eventual accession to the throne, the title will merge with the crown and can be regranted anew to Edward.  
George VI also gave Philip the titles of Earl of Merioneth and Baron Greenwich in the Peerage of the United Kingdom shortly before his marriage to Princess Elizabeth on November 20 1947.
The youngest of the Queen and Dukes four children, the Earl of Wessex has already followed in his fathers footsteps by taking on many of his patronages. 
He is trustee of the prestigious Duke of Edinburghs Award Scheme, patron of the Edinburgh International Festival, and has already taken on patronages reflecting Prince Philips loves of seafaring and sport.
The decision to give Edward the title was taken in recognition of his work with, and commitment to, the Duke of Edinburgh’s Award – as well as chairman of The Duke of Edinburgh’s International Award.
Edward’s wife the Countess of Wessex will eventually become the Duchess of Edinburgh – a courtesy title which was held by the Queen.